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I wrote an intro to this here:
http://forumserver.twoplustwo.com/sh...4251&page=
It is a bit mathy, but hopefully gives you a taste of the difference the historically understood "time as a parameter in the Schrodinger equation" and "time in the Wheeler-DeWitt equation", which was mentioned in the article you cite.
Also -- that guy Carlo Rovelli who was referenced in that article is my hero.
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Sorry, afraid you lost me at covariant :]
How wikipedia defines it in the first paragraph and the way you use it don't seem to mesh too well for me. Perhaps it'd make more sense if I understood past the first paragraph of the wikipedia entry